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A multigrid platform for realtime motion computation with discontinuitypreserving variational methods
 International Journal of Computer Vision
, 2006
"... Abstract. Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such ad ..."
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Cited by 57 (15 self)
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Abstract. Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for realtime performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that realtime performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude.
Towards Ultimate Motion Estimation: Combining Highest Accuracy with RealTime Performance
, 2005
"... Although variational methods are among the most accurate techniques for estimating the optical flow, they have not yet entered the field of realtime vision. Main reason is the great popularity of standard numerical schemes that are easy to implement, however, at the expense of being too slow for re ..."
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Cited by 44 (10 self)
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Although variational methods are among the most accurate techniques for estimating the optical flow, they have not yet entered the field of realtime vision. Main reason is the great popularity of standard numerical schemes that are easy to implement, however, at the expense of being too slow for realtime performance. In our paper we address this problem in two ways: (i) We present an improved version of the highly accurate technique of Brox et al. [9]. Thereby we show that a separate robustification of the constancy assumptions is very useful, in particular if the 1norm is used as penalizer. As a result, a method is obtained that yields the lowest angular errors in the literature. (ii) We develop an efficient numerical scheme for the proposed approach that allows realtime performance for sequences of size 160 × 120. To this end, we combine two hierarchical strategies: A coarsetofine warping strategy as implementation of a fixed point iteration for a nonconvex optimisation problem and a nonlinear full multigrid method – a so called full approximation scheme (FAS) – for solving the highly nonlinear equation systems at each warping level. In the experimental section the advantage of the proposed approach becomes obvious: Outperforming standard numerical schemes by two orders of magnitude frame rates of six high quality flow fields per second are obtained on a 3.06 GHz Pentium4 PC.
Piecewisesmooth dense optical flow via level sets
 Vision and Image Analysis Laboratory, School of Electrical Engineering, Tel Aviv
, 2005
"... We propose a new algorithm for dense optical flow computation. Dense optical flow schemes are challenged by the presence of motion discontinuities. In state of the art optical flow methods, oversmoothing of flow discontinuities accounts for most of the error. A breakthrough in the performance of op ..."
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Cited by 26 (3 self)
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We propose a new algorithm for dense optical flow computation. Dense optical flow schemes are challenged by the presence of motion discontinuities. In state of the art optical flow methods, oversmoothing of flow discontinuities accounts for most of the error. A breakthrough in the performance of optical flow computation has recently been achieved by Brox et al. Our algorithm embeds their functional within a two phase active contour segmentation framework. Piecewisesmooth flow fields are accommodated and flow boundaries are crisp. Experimental results show the superiority of our algorithm with respect to alternative techniques. We also study a special case of optical flow computation, in which the camera is static. In this case we utilize a known background image to separate the moving elements in the sequence from the static elements. Tests with challenging real world sequences demonstrate the performance gains made possible by incorporating the static camera assumption in our algorithm. 1
A Survey on Variational Optic Flow Methods for Small Displacements
, 2005
"... Optic flow describes the displacement field in an image sequence. Its reliable computation constitutes one of the main challenges in computer vision, and variational methods belong to the most successful techniques for achieving this goal. Variational methods recover the optic flow field as a minimi ..."
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Cited by 14 (0 self)
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Optic flow describes the displacement field in an image sequence. Its reliable computation constitutes one of the main challenges in computer vision, and variational methods belong to the most successful techniques for achieving this goal. Variational methods recover the optic flow field as a minimiser of a suitable energy functional that involves data and smoothness terms. In this paper we present a survey on different model assumptions for each of these terms and illustrate their impact by experiments. We restrict ourselves to rotationally invariant convex functionals with a linearised data term. Such models are appropriate for small displacements. Regarding the data term, constancy assumptions on the brightness, the gradient, the Hessian, the gradient magnitude, the Laplacian, and the Hessian determinant are investigated. Local integration and nonquadratic penalisation are considered in order to improve robustness under noise. With respect to the smoothness term, we review a recent taxonomy that links regularisers to diffusion processes. It allows to distinguish five types of regularisation strategies: homogeneous, isotropic imagedriven, anisotropic imagedriven,
An iterative scheme for motionbased scene segmentation
 In Workshop on Dynamical Vision (ICCV
, 2009
"... We present an approach for dense estimation of motion and depth of a scene containing a multiple number of differently moving objects with the camera system itself being in motion. The estimates are used to segregate the image sequence into a number of independently moving objects by assigning the ..."
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Cited by 2 (0 self)
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We present an approach for dense estimation of motion and depth of a scene containing a multiple number of differently moving objects with the camera system itself being in motion. The estimates are used to segregate the image sequence into a number of independently moving objects by assigning the object hypothesis with maximum a posteriori (MAP) probability to each image point. Different to previous approaches in 3dimensional (3D) scene analysis, we tackle this task by first simultaneously estimating motion and depth for a salient set of feature points in a recursive manner. Based on the evolving set of estimated motion profiles, the scene depth is recovered densely from spatially and temporally separated views. Given the dense depth map and the set of tracked motion estimates, the likelihood of each image point to belong to one of the distinct motion profiles can be determined and dense scene segmentation can be performed. Within our probabilistic model the expectationmaximization (EM) algorithm is used to solve the inherent missing data problem. A Markov Random Field (MRF) is used to express our expectations on spatial and temporal continuity of objects. 1.
unknown title
, 1600
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy.
Optical Flow at Occlusion
"... Abstract—We implement and quantitatively/qualitatively evaluate two optical flow methods that model occlusion. The Yuan et al. method [1] improves on the Horn and Schunck optical flow method at occlusion boundaries by using a dynamic coefficient (the Lagrange multiplier α) at each pixel that weighs ..."
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Abstract—We implement and quantitatively/qualitatively evaluate two optical flow methods that model occlusion. The Yuan et al. method [1] improves on the Horn and Schunck optical flow method at occlusion boundaries by using a dynamic coefficient (the Lagrange multiplier α) at each pixel that weighs the smoothness constraint relative to the optical flow constraint, by adopting a modified scheme to calculate average velocities and by using a “compensating ” iterative algorithm to achieve higher computational efficiency. The Niu et al. method [2] is based on a modified version of the Lucas and Kanade optical flow method, that selects local intensity neighbourhoods, spatially and temporally, based on pixels that are on different sides of an occlusion boundary and then corrects any erroneous flow computed at occlusion boundaries. We present quantitative results for sinusoidal sequence with a known occlusion boundary. We also present qualitative evaluation of the methods on the Hamburg Taxi sequence and and the Trees sequence. Keywords2D optical flow, discontinuous optical flow, optical flow at occlusion boundaries, quantitative and qualitative error analysis. I.
Probability, Networks and Algorithms The multigrid image transform
, 2005
"... CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms. ..."
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CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms.
Application of the Hodge Helmholtz . . .
, 2005
"... The computation of the 2D motion field from a sequence of images is one of the key tasks of many vision systems. Analysis and interpretation of flow fields is in general a complex task. One of the most interesting problems is to locate critical points in the motion field. The main theme of this the ..."
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The computation of the 2D motion field from a sequence of images is one of the key tasks of many vision systems. Analysis and interpretation of flow fields is in general a complex task. One of the most interesting problems is to locate critical points in the motion field. The main theme of this thesis is the identification of critical points in motion fields, which have a physical significance for the corresponding application. The discrete Hodge Helmholtz decomposition is a vector decomposition algorithm which is used in this thesis for locating critical points in a motion field. Automatic